Froggy Jumps
Vectors IV Lowersixth Science MathematicsOnline version
Challenge your understanding of lines in 2D.
1
What is the vector form of a line through point r0 with direction v?
2
Which parameter t represents in the vector equation?
3
In the vector form r = r0 + t v, what is r0?
4
What is the parametric equation form of a line through (1,2) with direction (3,4)?
5
For the line x = 2 + 5t, y = -1 + t, what is the direction vector?
6
Which equation is a Cartesian (symmetric) form of a line in 2D?
7
Symmetric form for a line with direction (a,b) is:
8
If a line passes through (2,3) and is parallel to vector (4, -2), its symmetric form is:
9
What is the angle between two lines with direction vectors u and v?
10
If two lines have direction vectors (1,0) and (0,1), the angle between them is:
11
A line through point p with direction vector d is called:
12
Equation of a line through (a,b) parallel to vector (p,q) is:
13
Which form is most direct for a line’s direction?
14
The point-slope form is best described as:
15
In parametric form, how is t interpreted?
16
Which quantity remains constant along a line in symmetric form?
17
If a line has equation x = 3, y = t, what is this line’s direction?
18
The vector equation of a line is most useful for:
19
What is required to define a line in 3D from a 2D perspective?
20
Which form expresses a line using a common point and direction?
21
Angle between lines can be found using:
22
If line1 has direction (2,3) and line2 (4,6), the angle is:
23
How do you obtain a line through P parallel to v?
24
Symmetric form is undefined if:
25
Which is NOT a line form?
26
A line with equation r = (1,2,3) + t(4,0,1) lies in:
27
In 2D, the vector direction is perpendicular to:
28
Parametric form allows easy computation of:
29
The angle between lines is smallest when θ is:
30
To express a line through (a,b) with slope m, use:
31
Which form is best for parallelism tests?
32
A line parallel to v through r0 uses:
33
If v = (0,5), the line is:
34
The dot product in angle formula yields:
35
Which form directly shows the direction vector?
36
Line through (0,0) parallel to (3,4) is:
37
Which statement is true?
38
Symmetric form requires:
39
What does r0 + t v describe?
40
Which form is most compact for 3D lines?
41
A line has direction (1,-2). Its slope is:
42
To check parallelism, compare:
43
Which operation gives angle between lines 2D?
44
If two lines have same direction, they are:
45
What is a key feature of parametric equations?
46
Line through P with direction v can be written as:
47
When is symmetric form undefined in x-division?
48
Which form directly encodes both point and direction?
49
Which is a property of a line’s direction?
50
Which is the Cartesian (symmetric) form of a line through (x1, y1) with direction ratios a, b?
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Functions and Structures of the skin
